State Geometrical meaning of roots of equation

Geometrical meaning of Zeros

The quadratic equation whose roots are the arithmetic mean and the harmonic mean of the roots of the equation x^(2)+7x-1=0 is

State Geometrical relation of Excenters?

If the arithmetic mean of the roots of quadratic equation is (8)/(5) and the arithmetic mean of their reciprocals is (5)/(8) then the equation is

If the arithmetic mean of the roots of x^(2)-2ax+b=0 is A and the geometric mean of the roots of x^(2)-2bx+a^(2)=0 is G, then

IF the arithmetic mean of the roots of a quadratic equation is 8/5 and the arithmetic mean of their reciprocals is 8/7 then the equation is

The harmonic mean of two numbers is 4. Their arithmetic mean A and the geometric mean A and the geometric mean G satisfy the relation 2A + G^2 = 27 . Find the numbers.

The roots alpha and beta of a quadratic equation are the square of two consecutive natural numbers. The geometric mean of the two roots is 1 greater than the difference of the roots. If alpha and beta lies between the roots of x^2-cx+ 1 = 0 then find the minimum integral value of c.